From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8568 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Partial functors .. Date: Wed, 18 Mar 2015 03:03:12 -0400 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1426681758 22840 80.91.229.3 (18 Mar 2015 12:29:18 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 18 Mar 2015 12:29:18 +0000 (UTC) To: David Yetter , Categories list Original-X-From: majordomo@mlist.mta.ca Wed Mar 18 13:29:10 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YYD5v-00086O-Q1 for gsmc-categories@m.gmane.org; Wed, 18 Mar 2015 13:29:07 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:44027) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YYD5D-0003pR-Hy; Wed, 18 Mar 2015 09:28:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YYD5C-0006TD-0T for categories-list@mlist.mta.ca; Wed, 18 Mar 2015 09:28:22 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8568 Archived-At: One had better take care to note explicitly how to compose maps to = and from the newly adjoined "zero object", if following Yetter's idea, > The previous suggestion of considering functors to D + 1 was a false st= art > for reasons Fred and Uwe pointed out, but it suggests a better approach= : = > consider functors to the category D~ formed from D by freely adjoining = a > zero object. Arrows not in S now have somewhere to go (the zero arrow > with the appropriate source and target). For, given a and b objects in D and writing z for the newly adjoined zero= object, what are we to take for compositions a --> * --> b ? Or were we = also to adjoin "zero maps" z_(a,b) to each existing homset D(a, b), and = then set these compositions all equal to those new zero maps? That suggests Yetter really meant to propose forming the free *pointed* = category with zero object freely engendered by D ... or maybe that's what= = his words already meant to convey? Apologies if I was deaf to that tone := -) . Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]